Diagnosing solar wind forecast errors

Harriet Turner – h.turner3@pgr.reading.ac.uk

The solar wind is a continual outflow of charged particles that comes off the Sun, ranging in speed from 250 to 800 km s-1. During the first six months of my PhD, I have been investigating the errors in a type of solar wind forecast that uses spacecraft observations, known as corotation forecasts. This was the topic of my first paper, where I focussed on extracting the forecast error that occurs due to a separation in the spacecraft latitude. I found that up to a latitudinal separation of 6 degrees, the error contribution was approximately constant. Above 6 degrees, the error contribution increases as the latitudinal separation increases. In this blog post I will explain the importance of forecasting the solar wind and the principle behind corotation forecasts. I will also explain how this work has wider implications for future space missions and solar wind forecasting.

The term “space weather” refers to the changing conditions in near-Earth space. Extreme space weather events can cause several effects on Earth, such as damaging power grids, disrupting communications, knocking out satellites and harming the health of humans in space or on high-altitude flights (Cannon, 2013). These effects are summarised in Figure 1. It is therefore important to accurately forecast space weather to help mitigate against these effects. Knowledge of the background solar wind is an important aspect of space weather forecasting as it modulates the severity of extreme events. This can be achieved through three-dimensional computer simulations or through more simple methods, such as corotation forecasts as discussed below.

Figure 1. Cosmic rays, solar energetic particles, solar flare radiation, coronal mass ejections and energetic radiation belt particles cause space weather. Subsequently, this produces a number of effects on Earth. Source: ESA.

Solar wind flow is mostly radial away from the Sun, however the fast/slow structure of the solar wind rotates round with the Sun. If you were looking down on the ecliptic plane (where the planets lie, at roughly the Sun’s equator), then you would see a spiral shape of fast and slow solar wind, as in Figure 2. This makes a full rotation in approximately 27 days. As this rotates around, it allows us to use observations on this plane as a forecast for a point further on in that rotation, assuming a steady-state solar wind (i.e., the solar wind does not evolve in time). For example, in Figure 2, an observation from the spacecraft represented by the red square could be used as a forecast at Earth (blue circle), some time later. This time depends on the longitudinal separation between the two points, as this determines the time it takes for the Sun to rotate through that angle.

Figure 2. The spiral structure of the solar wind, which rotates anticlockwise. Here, STA and STB are the STEREO-A and STEREO-B spacecraft respectively. The solar wind shown here is the radial component. Source: HUXt model (Owens et al, 2020).

In my recent paper I have been investigating how the corotation forecast error varies with the latitudinal separation of the observation and forecast points.  Latitudinal separation varies throughout the year, and it was theorised that it should have a significant impact on the accuracy of corotation forecasts. I used the two spacecraft from the STEREO mission, which are on the same plane as Earth, and a dataset for near-Earth. This allowed for six different configurations to compute corotation forecasts, with a maximum latitudinal separation of 14 degrees. I analysed the 18-month period from August 2009 to February 2011 to help eliminate other affecting variables. Figure 3 shows the relationship between forecast error and latitudinal separation. Up to approximately 6 degrees, there is no significant relationship between error and latitudinal separation. Above this, however, the error increases approximately linearly with the latitudinal separation.

Figure 3. Variation of forecast error with the latitudinal separation between the spacecraft making the observation and the forecast location. Error bars span one standard error on the mean.

This work has implications for the future Lagrange space weather monitoring mission, due for launch in 2027. The Lagrange spacecraft will be stationed in a gravitational null, 60degrees in longitude behind Earth on the ecliptic plane. Gravitational nulls occur when the gravitational fields between two or more massive bodies balance out. There are five of these nulls, called the Lagrange points, and locating a spacecraft at one reduces the amount of fuel needed to stay in position. The goal of the Lagrange mission is to provide a side-on view of the Sun-Earth line, but it also presents an opportunity for consistent corotation forecasts to be generated at Earth. However, the Lagrange spacecraft will oscillate in latitude compared to Earth, up to a maximum of about 5 degrees. My results indicate that the error contribution from latitudinal separation would be approximately constant.

The next steps are to use this information to help improve the performance of solar wind data assimilation. Data assimilation (DA) has led to large improvements in terrestrial weather forecasting and is beginning to be used in space weather forecasting. DA combines observations and model output to find an optimum estimation of reality. The latitudinal information found here can be used to inform the DA scheme how to better handle the observations and to, hopefully, produce an improved solar wind representation.

The work I have discussed here has been accepted into the AGU Space Weather journal and is available at https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2021SW002802.


Cannon, P.S., 2013. Extreme space weather – A report published by the UK royal academy of engineering. Space Weather, 11(4), 138-139.  https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/swe.20032

ESA, 2018. https://www.esa.int/ESA_Multimedia/Images/2018/01/Space_weather_effects 

Owens, M.J., Lang, M.S., Barnard, L., Riley, P., Ben-Nun, M., Scott, C.J., Lockwood, M., Reiss, M.A., Arge, C.N. & Gonzi, S., 2020. A Computationally Efficient, Time-Dependent Model of the Solar Wind for use as a Surrogate to Three-Dimensional Numerical Magnetohydrodynamic Simulations. Solar Physics, 295(3), https://doi.org/10.1007/s11207-020-01605-3